Google: We Care About URL & Last Modification Date

Google's John Mueller said on Twitter this morning that Google doesn't really care much about the priority field in the XML Sitemap, but they do care about the URL and last modification date. Here is the tweet:

We know Google doesn't care about the priority field, Google has said that time and time again.

But Gary Illyes back in 2015 said Google ignores last mod date in Sitemaps for the most part. Here, John seems to be implying the opposite.

It might be that Google actually has their own last modification date based on looking at the page on date X and then on date Y and noticing a modification. Maybe that is what John is talking about. Or maybe Google now does look at the last modification date in the sitemaps file?